WASHINGTON (AP) _ Opponents of a plan by President Reagan to sell the Federal Housing Administration to private bidders and cut housing subsidies in the 1987 fiscal year vowed Saturday to fight the proposal in Congress.

''It's nuts. Why doesn't he sell the Washington Monument?'' said Mayor Edward I. Koch of New York. ''We haven't seen this kind of turning your back on low income people since Marie Antoinette,'' the mayor said, referring to the French queen beheaded during the French Revolution. The queen, told that her people had no bread, said ''Let them eat cake,'' according to tradition.

Rep. Barney Frank, D.-Mass, said Reagan's proposal ''is appalling but not surprising.''

''We have a serious housing crisis in many areas, and it is being exacerbated by Reagan Administration policies,'' said Frank, who is chairman of the House governmental operations subcommittee on housing and unemployment. He predicted that Congress would not approve Reagan's plan.

Since the FHA was founded in 1934 to offset economic hardships during the Depression, it has provided mortage insurance to 51 million Americans, many of whom might not have otherwise been able to afford homes.

An administration official confirmed a report published in Saturday editions of The New York Times that confidential documents were submitted last week to Housing and Urban Development Secretary Samuel R. Pierce Jr. proposing sale of the FHA to ''private bidders'' in the ''private sector'' by the end of 1989. The official spoke on condition he not be identified.

Pierce's spokesman, Leonard Burchman, said that department officials would have no comment before Monday.

Almost half of the 11,400 people employed by the department work for the FHA or on FHA projects. The organization, which produced a profit of $9.4 million last year, serves as a giant mortgage insurance company.

Other points in the Reagan plan, the administration source said, include:

-Canceling $6.2 billion of the $9.9 billion that Congress recently appropriated for housing for low and moderate income people.

-Requiring state and local authorities to pay half the administrative costs of the main federal program giving rental assistance to the poor. The U.S. government now pays all those costs.

-Ending the inflation adjustment for federal housing subsidies.

-Asking Congress to allow the use of Social Security numbers to verify that peole living in federally subsidized housing meet income requirements.

-Ending federal grants to subsidize construction or for rehabilitation of rental housing in low and moderate-income neighborhoods.

-Freezing federal subsidies for running local public housing projects at 1986 levels.

-Ending urban development action grants, designed to assist distressed urban areas.

The sale of the FHA could not take place without congressional approval, which critics of the plan promised to fight.

Peter H. Bell, executive director of the Washington-based National Housing Rehabilitation Association, called it ''an outrageous proposal.''

''I can't fathom them getting this proposal through Congress. But we'll certainly make sure they don't,'' said Bell, whose organization, founded in 1970, monitors government housing policy.

Robert W. Maffin, executive director of the National Association of Housing and Redevelopment Officials, predicted the package would not clear Congress ''without some major changes.''

''The elderly, the young, the farmers, there are literally hundreds of groups of people in the United States who need help in securing decent housing,'' he said.

Paul Scheiber, executive director of the Public Housing Authorities Directors Association, described the plan as ''miserable. I think it's insensitive. I think it's penny-wise and dollar-foolish.''

''It is criminal to have a huge block of public housing without providing enough to repair it,'' said Scheiber, whose Washington based organization, founded in 1979, represents 600 members public housing authorities throughout the United States.